The HIV-1/AIDS pandemic continues to spread unabated worldwide, and no vaccine exists within our grasp. Effective antiretroviral therapy (ART) has been developed, but ART cannot clear the virus from the infected patient. A cure for HIV-1 is badly needed to stop both the spread of the virus in human populations and disease progression in infected individuals. A safe and effective cure strategy for human immunodeficiency virus (HIV) infection will require multiple tools, and appropriate animal models are tools that are central to cure research. An ideal animal model should recapitulate the essential aspects of HIV pathogenesis and associated immune responses, while permitting invasive studies, thus allowing a thorough evaluation of strategies aimed at reducing the size of the reservoir (functional cure) or eliminating the reservoir altogether (sterilizing cure). Since there is no perfect animal model for cure research, multiple models have been tailored and tested to address specific quintessential questions of virus persistence and eradication. The development of new non-human primate and mouse models, along with a certain interest in the feline model, has the potential to fuel cure research. In this review, we highlight the major animal models currently utilized for cure research and the contributions of each model to this goal.